I am going to substitute the word "favorite" for the word "best" and the words "least favorite" for the word "worst."
Favorite quest
My favorite single quest is "Fargoth's Hiding Place." It always tickles me, no matter how many times I do it. I love spying on Fargoth from the Lighthouse. That is one of the most clever quests in the game, in my opinion. I would put it in my personal "Top 20 Bethesda Quests" list. Honorable mention goes to "Hentus Needs Pants."
As far as quest lines go, I like the main quest. It is the only genuinely good main quest Bethesda has ever written, in my opinion. Thirteen years later I still am uncertain whether my character was actually the Nerevarine or whether she was merely an impostor who was being used for political gain. Fantastic writing.
Favorite character
Dagoth Ur. He's the only antagonist in a Bethesda game whose motives are understandable to me. The antagonists in the other just seem to be menacing Tamriel because the plot demands conflict. I could almost sympathize with Dagoth Ur in some ways, and I think that makes for a good "villain."
Favorite enemy
Skeletons. Skeletons are an RPG classic. I never tire of sword-wielding skeletons. Or bow-wielding skeletons. Or any skeletons. As long as they're skeletons and I have to fight them, I'm fine.
Favorite game feature
Chance of failure. I love the idea that my character might fail at casting a spell, fail at making a potion, fail at connecting with a sword. The fact that this is based on my character's skill and not my own makes my character feel more real to me.
Favorite concept
The non-linear, open-world approach that is standard in this series. This is probably the main thing that made me love Morrowind (and the series itself). After playing Morrowind back in 2002 I found I couldn't go back to Bioware-style linear, story-based games with game worlds that feel like they take place in large rooms and corridors.
Favorite faction
Tribunal Temple. It's one of the few factions in an Elder Scrolls game that isn't centered merely around killing things. We spend a lot of time curing people of diseases, recovering artifacts, feeding hungry people. It is a refreshing change from the usual adolescent "kill this, kill that" approach most RPG quests (and especially Bethesda quests) force on us. I loved doing the pilgrimage quests.
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Least favorite quest
"The Runaway Slave." It's a real pain to escort Reeh-Jah from the Molag Amur region down to Ebonheart. A real pain.
Least favorite character
Sellus Gravius. Everything about this guy rubs me the wrong way. I don't like Imperials to begin with and I especially don't care for officious authority figures.
Least favorite enemy
Cliff Racers. It's the sound. It's everywhere you go. They might be miles away or they might be right on top of you. You have to stop what you';re doing an find out if you're about to be attacked or if they're too far away to notice you. They're everywhere, so you have to do it again...and again...and again...and again...
Least favorite game feature
The fact that the NPCs stand in the same place all day and all night. This was one of the big criticisms Daggerfall fans made of Morrowind when I got here, and for once I agree with them.
Least favorite concept
Leveling. New enemies stop appearing at about level 22. I don't know what they were thinking with this. It must never have occurred to anybody at Bethesda that some of us might actually play our characters past level 25. For all its problems I think Oblivion's enemy level-scaling was an improvement.
Least favorite faction
Imperial Legion. I don't like Imperials and I don't like the Empire. I can't bring myself to do this quest line.